Abstract
Coral reefs are highly valued ecosystems currently threatened by both local and global stressors. Given the importance of coral reef ecosystems, a Bayesian network approach can benefit an evaluation of threats to reef condition. To this end, we used data to evaluate the overlap between local stressors (overfishing and destructive fishing, watershed-based pollution, marine-based pollution, and coastal development threats), global stressors (acidification and thermal stress), and management effectiveness with indicators of coral reef health (live coral index, live coral cover, population bleaching, colony bleaching, and recently killed corals). Each of the coral health indicators had Bayesian networks constructed globally and for Pacific, Atlantic, Australia, Middle East, Indian Ocean, and Southeast Asia coral reef locations. Sensitivity analysis helped evaluate the strength of the relationships between different stressors and reef condition indicators. The relationships between indicators and stressors were also evaluated with conditional analyses of linear and nonlinear interactions. In this process, a standardized direct effects analysis was emphasized with a target mean analysis to predict changes in the mean value of the reef indicator from individual changes to the distribution of the predictor variables. The standardized direct effects analysis identified higher risks in the Middle East for watershed-based pollution with population bleaching and in Australia for overfishing and destructive fishing with living coral. For thermal stress, colony bleaching and recently killed coral in the Indian Ocean were found to have the strongest direct associations along with living coral in the Middle East. For acidification threat, Australia had a relatively strong association with colony bleaching, and the Middle East had the strongest overall association with recently killed coral, although extrapolated spatial data were used for the acidification estimates. The Bayesian network approach helped to explore the relationships among existing databases used for policy development in coral reef management by examining the sensitivity of multiple indicators of reef condition to spatially distributed stress.
Keywords: Coral reefs, Bayesian belief networks, Ecological integrity, Climate change, Marine pollution
EDITOR’S NOTE:
This article is part of the special series “Applications of Bayesian Networks for Environmental Risk Assessment and Management” and was generated from a session on the use of Bayesian networks (BNs) in environmental modeling and assessment in 1 of 3 recent conferences: SETAC North America 2018 (Sacramento, CA, USA), SETAC Europe 2019 (Helsinki, Finland), and European Geosciences Union 2019 (Vienna, Austria). The 3 sessions aimed at showing the state-of-the art and new directions in the use of BN models in environmental assessment, focusing on ecotoxicology and water quality modeling. This series aims at reflecting the broad applicability of BN methodology in environmental assessment across a range of ecosystem types and scales, and discusses the relevance for environmental management.
INTRODUCTION
The worldwide decline and risk of extinction of coral reefs are especially distressing given their role in supporting marine ecosystems and biological diversity and their value to human society. For many local and global economies, coral reefs are important for delivering ecosystem services that have cultural, social, market, and nonuse value. Those values are continuously being investigated and better understood. Improved characterization of shoreline protection and recreation increased the estimated value of coral reefs from US$8000 per hectare per year in the 1997 estimate (Costanza et al. 1997) to $352 000 per hectare per year in the 2011 estimate (Costanza et al. 2014). However, during the same time period and using the 2011 unit values, the global estimated value of coral reefs decreased due to the areal loss of coral reefs (Costanza et al. 2014). Despite the value of coral reefs to local and global societies, they currently face increased extinction risks from anthropogenic sources of stressors (Carpenter et al. 2008) amounting to a “decision crisis” to prevent continuing losses of reef structure and function (NASEM 2019).
Coral reefs face stressors that are both local and increasingly global in nature (Hughes and Connell 1999; Fitt et al. 2001; Fabricius 2005; Hoegh-Guldberg et al. 2007; Knowlton and Jackson 2008; Ban et al. 2014; França et al. 2020). Shallow-water reefs are exposed to a variety of pollutants from human activities in the watershed and coastal zone, including sediments, contaminants, and nutrients that adversely affect coral survival, growth, and reproduction. Simultaneously, reefs are affected by global increases in ocean temperature beyond their natural range and by acidity that reduces their capacity to accrete carbonate for building skeletal framework. Early response of stony corals to many stresses is “bleaching,” which is the loss of symbiotic algae that are photosynthetic and provide energy to the coral (Putnam et al. 2017). Even if bleached tissue initially survives and colonies regain the photosynthetic algae, bleaching is often followed by increased susceptibility to disease, loss of tissue (morbidity), and ultimately colony mortality. Recovery of coral is inhibited by competition with macroalgal growth for colonizable surfaces. Macroalgae gain an advantage in the competition for space in areas of nutrient pollution and overharvesting of herbivorous fish that normally crop the algae (Roberts 1995). Accelerating global changes are expected to exacerbate these challenges, particularly in regions with growing human populations and limited management capacity (Anthony et al. 2015). Ocean acidification and rising temperatures, for example, are expected to favor macroalgae growth and diminish the capacity of coral reefs to recover from bleaching and other episodic events (Pandolfi et al. 2003; Ateweberhan et al. 2013). Recovery of colonies and reestablishment of reefs is made more challenging because of slow colony growth rates and deteriorating reef communities. Accounting for the condition and threats to coral reefs can help stem the ongoing damage to these systems through increased awareness and management opportunities.
Given the importance of coral reef ecosystems and the increasing availability of data, a risk-based approach can be beneficial for summarizing existing information on coral reef endpoints and stressors. Here, the information in 2 well-known databases, the World Resources Institute (WRI) Reefs at Risk threat maps to coral reefs (Burke et al. 2011) and condition information from a group called Reef Check (Hodgson and Liebeler 2002), are analyzed for potential relationships. These data sets were selected because of their comprehensiveness and wide use for assessing reef health and for their potential to relate coral indicators to global and local stressors and management effectiveness. Spatial variations between threat levels and coral reef condition were screened for coral reef locations with biological monitoring data from across the world. The probabilistic properties of the models that were developed create a clearer picture of the uncertainties in overlap between stressor types and intensities and reef condition from in situ observations.
Bayesian networks (BNs) were chosen as the modeling platform because of their capacity to handle large data sets and nonlinearities, make inferences, and examine uncertainties. Bayesian networks graphically encode a joint probability distribution among variables (Pearl 1988). A BN represents the conditional independence between the variables in the probability distribution while the variables connected to one another each have a conditional probability distribution to locally represent the strength of their connections. Bayesian networks are often used when uncertainties exist about the likely outcome for a variable in a system model and when inferences are optimally considered in an omnidirectional fashion (Conrady and Jouffe 2015). This contrasts with deterministic models that do not properly characterize risks and assume too much about the likely state of a variable conditioned on background knowledge. This is particularly important in environmental problems where uncertainty and noise in the data are expected and not exceptional. The uncertainties in the relationships among variables in a BN allow analysts to state what the most likely outcome would be but also represent the potential for other outcomes to occur, thereby preventing surprises in predictions.
A machine learning or automated approach was used in the present study to learn the network structure from data. One of the key benefits of an automated approach is the representation of the joint probability of the data and the covariance structure. Highly dependent variables are easily accommodated, and inferences can still be valid with almost any type of variable included.
Naïve Bayes classifiers and associated algorithms (e.g., tree augmented naïve Bayes, augmented naïve Bayes) are increasingly used in environmental science (Altartouri and Jolma 2013; Pawson et al. 2017; Lehikoinen et al. 2019; Sundar et al. 2019; Wiest et al. 2019). The present study focused on the influence of threats or management effectiveness on coral indicators. In this case, risk-based BNs were built with augmented naïve structures for a screening-level assessment of the risks to reef health indicators.
We compared candidate models and selected a global model, as well as a model for each region, for 5 different indicators of scleractinian (stony) coral condition. We then used the final models to assess the relative strength of stressors in relation to coral condition by focusing on direct effect statistics supported by other BN statistics and the functional form of the relationships between coral indicators and predictors, including stressors and management effectiveness. Although developed for coral reefs, the present analysis shows how BNs can be used for screening-level risk assessments with broad and complex spatial data sets of threat levels and resource condition monitoring data.
METHODS
Data sources
Several global assessment reports and monitoring systems exist for coral reef ecosystems established by a combination of academic, nongovernmental, and global governmental agencies. One of the more popular and comprehensive compendiums is the World Resource Institute’s (WRI) Reefs at Risk reports, which cover global and regional reef threats and condition (Burke et al. 2011). The WRI Reefs at Risk project periodically assesses the condition of coral reefs at regional to global scales and maintains databases of spatially explicit indicators of coral reef stressors such as overfishing and destructive fishing, and marine- and land-based sources of pollution. The WRI also has developed unique management tools for estimating the economic value of coral reefs (WRI 2007). Recent applications of the WRI data and approaches have led to significant changes in reef protection, particularly for designing marine protected zones.
Citizen science has emerged as an important data source in the protection of coral reefs through global biomonitoring efforts that augment and sometimes exceed the formal research and regulatory monitoring that has dominated reef condition assessments. Reef Check maintains a database of citizen monitoring of coral bleaching and condition in regions spanning Africa, the Middle East, Australia, Asia, and the Americas (Hodgson and Liebeler 2002). The global breadth of the Reef Check database makes it one of the largest for coral reef monitoring, and it is often used for determining the status of reefs, especially in areas lacking government-funded assessments. The Reef Check methods are peer reviewed by scientists but are designed to be maintained and implemented by divers with or without formal scientific training (Hodgson and Liebeler 2002). Teams are trained by Reef Check and receive certification for recording substrate types, sponges and rocks, fishes, live coral cover, recently killed coral, benthic algal abundance, and evidence of disease (Hodgson et al. 2006). Aside from coral reef endpoints, Reef Check volunteers record background information about the site, including the presence of boating, blast fishing, and coral harvesting. Reef Check data used in the present analysis were from 1998 (February 28 first measurement) to 2010 (December 28 last measurement).
Global and local threat maps and management effectiveness data from the WRI Reefs at Risk project were used to predict levels of different indicators of reef condition. Analysis focused on recent, not future, threats to match the time period of the Reef Check data. Spatial layers were used from WRI that fell under the headings of local threats (coastal development, watershed-based pollution, marine-based pollution and damage, overfishing and destructive fishing adjusted for management [OFadj]), global threats (thermal stress, ocean acidification based on aragonite saturation [Arag]), and management effectiveness. Two different thermal stress layers were used—one did not include bleaching in the calculation of thermal stress (to allow comparison with bleaching of coral colonies and populations) and the other included bleaching. For all networks, the thermal stress layer that included bleaching observations was used except for the population and colony bleaching networks where the thermal stress layer without bleaching was used. The latter was received from WRI but was subsequently modified by aligning the data layer with the other data sets (using the Snap Raster function in ArcGIS [ESRI 2020]). The overfishing data included management effectiveness in its estimation to better examine management implications with reef condition. The spatial layers for threats from WRI were mostly ordinal scales (e.g., high, medium, low; none, severe). Additional information on WRI’s layers is contained in Burke et al. (2011). All threats and management effectiveness measurements were built with equitable methods globally.
The spatial layers are briefly described, but more information on the layers and the extrapolations done spatially can be found in Burke et al. (2011) and supporting information therein. Some of the spatial layers interact with coral reefs more directly than others. Acidification threat is built on the aragonite saturation state estimated from global models. Aragonite is the mineral that is most used by corals for building reefs. Increased CO2 will raise ocean acidity and block aragonite saturation to decrease the availability of minerals for coral reefs. Coastal development threat refers to the human activities that can damage corals. An example is nutrient enrichment from sewage that can stimulate algal growth that competes with corals for space. The threat levels of the layer are extrapolated from information on cities, ports, airports, and hotels, along with population pressures measured by density and growth of populations and tourism growth. Marine-based pollution looks at the threat from activities and infrastructure that can physically damage corals. It is built from sea-based infrastructure, shipping transport lanes, and size of commercial and cruise ship ports. Overfishing and destructive fishing combines these 2 components into 1 threat layer. Overfishing is based on the anticipated demand for seafood from coastal population centers based on coastal population density along with known fishing regions such as shallow areas of the continental shelf. Destructive fishing is based on reported or known areas where blast and poison fishing occur. Overfishing can disrupt food webs that maintain coral reef community structure and function and remove herbivorous fishes that graze on algae that compete with corals for space. Thermal stress is based on satellite measures for ocean warming events combined with bleaching occurrences. Thermal stress can lead to coral bleaching from heat stress in the warmer waters and eventually mortality if the corals do not recover from the bleaching event. Watershed-based pollution threat measures pollutant runoff threats and is based on erosion models with a plume dispersion model to extend threats outward into the ocean and was calibrated with satellite observations. Nutrients from land runoff can also stimulate algal growth but sediment can smother reefs and block sunlight to algal symbionts. Finally, management effectiveness was based on expert review of management in marine protected areas around the world. The overfishing and destructive fishing threat levels are reduced at higher levels of management effectiveness. Further details can be found in Burke et al. (2011) and supporting information therein.
Direct condition measures on coral species were used from the Reef Check database for comparison with the WRI stressor and management effectiveness databases. Coverage of Reef Check monitoring was global, so WRI regional designations (Burke et al. 2011) were applied to define the regional areas for assessment (Figure 1). Five condition measures were chosen. The live coral index (LCI) is a stony coral index calculated by the percent live coral divided by the sum of the percent live and percent recently killed coral (Hodgson and Liebeler 2002). Live coral cover (LiveCoral) is the percent of the substrate that consists of live (hard or reef-building) stony coral tissue. Population bleaching (PopBleach) is the percentage of the overall reef area on a transect that is bleached, whereas colony bleaching (ColBleach) is the mean percentage of bleaching in each of the affected coral colonies. Recently killed coral (DeadCoral) includes corals that have died in the last year but still have an identifiable standing structure. Units for each of these variables are in percentages for each station surveyed. Additional information on condition measurements, sampling design, and protocols can be obtained from Reef Check (Hodgson et al. 2006). Procedures and quality assurance for data used in the present analysis are available at websites for Reef Check (reefcheck.org) and WRI (wri.org).
Figure 1.
Reef Check sampling location sites and areas color coded into WRI regions: Purple = Atlantic (n = 568); blue = Pacific (n = 416); green = Australia (n = 161); red = Southeast Asia (n = 953); orange = Indian Ocean (n = 204); yellow = Middle East (n = 133). WRI = World Resources Institute.
Data preparation
Prior to initiating analysis, Reef Check data were examined for comments on the sampling and quality assurance flags. Sampling data flagged with coordinate errors and incomplete measurements of coral reef condition were excluded. Data points from Reef Check and spatial layers from WRI’s Reefs at Risk were imported into ArcGIS (ESRI 2020). Before joining the WRI layers and Reef Check data points, several modifications were made to the Reef Check database table. Data from Reef Check were excluded if the station coordinates were errantly located on land over the WRI countries spatial layer. For Reef Check data that contained more than 1 data point at a single station, the average at that site was taken for all endpoints except DeadCoral, PopBleach, and ColBleach where the maximum was used for conservatism. The WRI regions (Indian Ocean, Middle East, Australia, Southeast Asia, Pacific, and Atlantic) were assigned to each Reef Check assessment station. The monitoring data and threat layers were joined by extending the attribute table for the Reef Check data with attributes from the WRI layers. All threat and management effectiveness values intersected the corresponding Reef Check station in the resulting case file except for aragonite saturation. For aragonite saturation, the calculation used at each Reef Check station was the closest available value because some sites were located outside of the extent of the layer’s coverage, particularly in some coastal regions.
Bayesian network methods
The relationships among variables in the data were explored in Bayesian networks. Networks were constructed regionally and globally for each of the target variables (coral reef health endpoints) and multiple overlying threat scores. Candidates for each model were constructed with different discretizations that were identified with a genetic optimization algorithm with and without log-transforming the data first. For each region and coral reef endpoint, a final model was identified after considering different types of data handling (transformation) and different modifications to the structure learning score based on internal representation of the data and complexity of the connections. The final model was chosen based on the cross-validation precision for each of the candidate networks and was used for sensitivity analysis. Sensitivity analysis focused on 2 measures for overall sensitivity and sensitivity while considering the directionality of the relationships and causal assumptions. Graphs of the changes in the mean values of the coral reef variable from changes to the distribution of each of the predictors were also used. Finally, multiple sensitivity measures extending from linear to nonlinear were compared across the relationships between endpoints and stressors or management effectiveness for each region. All BN methods were implemented in Bayesialab 9.1 (Bayesia SAS 2020).
Discretization
In BNs, continuous variables are often discretized into intervals that reflect data availability, the distribution inherent in the data, or that maximize the sensitivity with another variable (Conrady and Jouffe 2015). A greater number of discretization intervals provide a better representation of the marginal distribution of a variable but can be a source of inaccurate inferences if the data do not sufficiently represent the probabilities for each of the intervals. The problem is compounded when parent node relationships must also be considered. Discretization methods must balance the data coverage as well as the representation of the distribution of the variable that is needed for analysis. Projected case frequencies for parent–child relationships were used for establishing the initial number of discretization thresholds in the model (Conrady and Jouffe 2015).
The LiveCoral, DeadCoral, PopBleach, ColBleach, and LCI variables were discretized using R2-GenOpt* procedures (Bayesia SAS 2020). R2-GenOpt* uses a minimum description length (MDL) measure to establish the number of discretization thresholds and genetic optimization for placing the thresholds on the scale of the data. Initially (with all data), 5 discretization thresholds were recommended by Bayesialab’s import wizard, and we established that a minimum of 3 discretization thresholds would be used. Some nodes obtained only 2 discretization thresholds with R2-GenOpt*, so these intervals were reconstructed with R2-GenOpt (absent the MDL measure) and 3 discretization levels. Prior to discretizing, the LCI variable’s values were subtracted from 1 to use the isolate zeroes function in establishing a discretization interval with all of the 1 values. Thus, interpretation of functional relationships of LCI with stressors is reversed (increasing LCI associated with increasing stressors implies greater risks rather than the intuitive relationship).
Five coral reef health endpoints were examined with 7 predictors. Each coral endpoint had a separate network created for the entire global data set and for 6 global regions for a finer scale spatial evaluation. The thermal stress predictors TB and TNoB included and did not include bleaching for estimating thermal stress, respectively. The TB node was used for nonbleaching coral health endpoints, and the TNoB endpoint was used for bleaching endpoints. The predictors each had ordinal variables. The management effectiveness and threat layers were treated as categorical and did not require discretization. The exception was that the acidification threat node was manually discretized based on WRI recommendations for high, medium, and low threat. The acidification threat layer contains aragonite saturation measurements that were categorized with the thresholds discussed in the WRI technical notes (i.e., aragonite saturation state Ω ≥ 3.25 [low threat], 3.0 ≥ Ω > 3.25 [medium threat], Ω < 3.0 [high threat]). The layer data used assume a 380-ppm stabilization level for CO2 to estimate aragonite saturation, which approximates the time period the threat layers were used to represent and the sampling time frame of the Reef Check data. Because there were few high-threat occurrences in the acidification threat layer, high threats were combined with medium threats to form a high/medium threat category that was designated as high. The Arag variables were made categorical (high and low threat states) and detached from the aragonite saturation state scale for placing the categories on a comparative scale with other threat indices. Discrete variables were reordered in Bayesialab to match the order of the numerical scales on coral reef endpoint nodes for easier interpretation of correlations.
All predictor variable states were given numerical values: 0 and 1 for the global stressors, and 0, 1, and 2 for the local stressors and management effectiveness when used for estimating mean values from probability distributions and for graphical comparisons of mean value relationships between predictors and coral indicators. The management effectiveness node contained 3 states for effective management (labeled as “Effective”), partially effective (labeled as “Partial”), and ineffective, no management, or no data (labeled as “Ineffective”) that were given corresponding values of 2, 1, and 0, respectively.
Bayesian network construction
Bayesian networks can be constructed using manual, automated, or combined methods, and automatic and manual learning methods exist for both the structure and relations of variables. Bayesian networks are often built manually in a causal fashion because causality is an important analog to conditional dependence and independence and enhances the interpretation of inferences. Deriving causal relationships between variables is often intuitive for domain experts, but the resulting network may not always provide a useful structure for evaluating a data set. Manual methods are useful for testing hypothesized causal structural assumptions and when structural domain knowledge is available. Causal models were initially created but were found to be intractable because of the number of parameters necessary for covering the probabilities and the difficulties determining directionality, given the proxy nature of the stressor layers and potential bidirectional relationships between predictors and coral reef condition (e.g., population increases caused by benefits from coral reefs, reef threats bring higher management efforts).
In the present article, we utilized score-based methods that are focused on representing the quality of the joint probability distribution while favoring simplicity in the structure to prevent overfitting (Jouffe and Munteanu 2001). This is accomplished by minimizing the MDL scores for the constructed networks (Conrady and Jouffe 2015). The augmented naïve method was favored due to its ability to identify covariation among the predictor variables. Augmented naïve analysis places the target variable as the root node and makes all other variables dependent on it for direct assessment of relationships. Additional dependencies among nontarget variables are considered given a direct dependency on the target (Aguilera et al. 2010). Overall, the augmented naïve model provides greater flexibility for inclusion of variables than manually constructed causal models and directly measures the strength of the relationships of predictor variables to the target. Thus, augmented naïve BNs were chosen for assessing the impacts of each of the individual local and global threats and management effectiveness with the coral health endpoints. The augmented naïve BNs were constructed through the supervised learning algorithms in Bayesialab. The basic structure for the augmented naïve networks includes a directed relationship from the target node to the predictors and possible relationships among the predictors (Figure A1 in Supplemental Data File 1). However, for some regions, low data availability favored the construction of completely naïve models.
For the augmented naïve BNs, a structural coefficient (SC) curve analysis was performed by varying a component’s weight in the MDL score over multiple networks, prior to accepting a model structure. For each endpoint and regional grouping, 1 candidate network was built with an optimized SC of 1. The SC of 1 represents a balance between optimizing the structure based on the data representation and the complexity of the network (Conrady and Jouffe 2015). For each region and endpoint and log- or nontransformation, 40 networks were constructed using augmented naïve Bayes for SCs ranging from 0.05 to 2, at intervals of 0.05. Besides a balanced SC of 1, candidate networks were extracted where the internal target precision was highest (outside of the zone of overfitting) with the data set and at the inflection point or zone of the SC vs. structure-to-target precision ratio curve before overfitting begins. Sometimes the inflection point was not clear, and in these cases, judgments were used to identify a balanced SC, but this was sometimes augmented by the location of higher internal precision values around the inflection area.
For each endpoint, global and region-specific networks were created for further assessment with individually rediscretized coral reef indicator nodes for each regional network to reflect the change in data. Individual augmented naïve networks were constructed with each coral condition endpoint as the target node but included the threats and management effectiveness as predictors. Moreover, networks were constructed for both regional and global (all data) partitions with and without log-transforming the data prior to discretization. After importing the data set and discretizing the created nodes, the multiquadrant analysis in Bayesialab automatically created separate BNs for each region. The regional networks were subsequently refined through rediscretization and the SC analysis above to reflect the condition of the available data. Coral reef indicator nodes in each of these networks were rediscretized following procedures used in the global networks. Machine-learned structures were used to construct 5 primary networks, each with the same variables except that coral reef endpoints were assessed individually as target variables for each network.
When quantitatively constructed from data sets, BNs often utilize the frequencies of occurrences for the data values to estimate probabilities through (un)conditional probabilities. Conditional probability tables (CPTs) were developed with the information in the data set based on the distribution of the data across the spatial layers for the entire globe or for different regions. For each constructed network, probabilities for each of the relationships were learned based on the overlap of the data behind the nodes in the geographic information system (GIS) database. Thus, conditional and marginal probabilities were learned from the database based on the number of cases present for each parent–child state relationship (or for each state for root nodes) from the coinciding sets of stressor, management effectiveness, and coral condition data at each station (Figure 1). Missing data that could not be temporally imputed from time series data at the same location were handled through structural expectation-maximization (Conrady and Jouffe 2015). To ensure coverage of all CPT cells, a single uniform prior sample was added across CPT rows in each network.
Model evaluation
Model evaluation occurred both during model construction to evaluate complexity and with the final accepted models to evaluate predictive performance. Model evaluation for determining the complexity weight in the MDL score was described above in the SC analysis. For candidate models extracted from the SC analysis, an out-of-sample validation method was used to select a final model. To evaluate overall predictive performance, a k-fold cross-validation was conducted on each candidate network (Conrady and Jouffe 2015). The optimal SC with highest internal precision, the SC at the inflection point, and an SC of 1 were all used as candidate models in a cross-validation analysis for each regional and coral health indicator model using both log-transformed and nontransformed data for the coral reef health indicator. The k-fold method shuffles the database and divides it into k pieces. The k–1 network predictions are tested with the final created segment. Discretization methods followed the original network for each tested network. This process was repeated 100 times and the results were aggregated over the output. The total precision value (in percent) was utilized to examine the confidence in the predictive ability of the model for each coral reef endpoint.
For the regional and global networks that were created, the various networks built with different SCs were selected and tested based on cross-validation accuracy levels, and a final candidate network was selected. Overall model predictive capabilities were compared across regions and endpoints based on the total precision from the 10-fold cross-validation (Kohavi 1995) for the final selected network for each endpoint and region. The selected augmented naïve Bayes networks were used in the sensitivity analysis for each of the regional networks and each coral reef health endpoint. Models were selected based on the number of discretization levels, the usage of data without transformation, and the total precision from cross-validation statistics. The models with more discretization thresholds were chosen when the total precision of candidate models was within 9%. If the number of discretization thresholds were equivalent, nontransformed data were used over log-transformed data if validation total precision was within 9% of each other. An SC not equal to 1 was chosen if it exceeded 9% of the overall precision above an otherwise preferred candidate model with an SC of 1 (to judge the value of increasing complexity or moving away from a balanced SC value). The final selected model for each regional data partition and endpoint was used for predicting the target coral reef condition indicator in the relationship analysis.
Relationship analysis
The nature and strength of the relationships between the nodes in the constructed networks were surveyed in various ways that are further described in Conrady and Jouffe (2015). A sensitivity analysis was used with mutual information (MI) for understanding the overall strength of the relationships between coral indicators and predictors. The MI analysis obtained a direct measure of the strength of the relationship between nodes through gain of information and reduction of uncertainty. The degree and type of functional relationship between parent and child node relationships was examined using standardized direct effects (SDE) combined with a target mean analysis (TMA). The SDE helped examine positive and negative linear relationships at the means of the target and predictor variable. The TMA highlighted nonlinear relationships where the SDE was not adequate and provided additional statistics for comparison, such as the percent difference in mean values along the TMA and the minimum mean value. Additional measures of association with the coral reef target nodes were also captured and recorded in the Supplemental Data, such as Pearson product-moment correlation coefficient R (PC), the Kullback-Leibler divergence (KLD), and the standardized and nonstandardized total effects (STE and TE) between each of the nodes and the coral reef endpoint node.
Multiple measures from information theory and classical statistics, which are further described in Conrady and Jouffe (2015), were used for each variable-to-variable relationship for the target node and predictors in each of the graphs. The MI provides evidence on how much uncertainty is reduced on 1 node when another node state is known and does not depend on linearity. The KLD measure also can be useful to measure the strength of relationships by comparing the information content of the probability distributions with and without the arc connecting 2 variables. Pearson correlation coefficient is calculated by the covariance between 2 nodes divided by the product of the standard deviation of each node. Total effect statistics are derivatives at the mean values of the prior distributions that are updated using the minimum cross-entropy (MinxEnt) method (Conrady and Jouffe 2015). A small change in the predictor is used to examine the TE as the change in the mean of the target node. Standardized versions of these measures (STE) are calculated by multiplying the TE by the quotient of the target and the predictor variables’ standard deviations. The PC value is equivalent to or closely aligned with the STE value and can assist in interpretation or communication due to its familiarity. We will focus on STE instead of PC in the present manuscript to reduce redundancy.
For TE analysis, the other predictors are permitted to covary with the predictor in question for an examination of the effects on the target node mean value with the joint probabilities considered. In a direct effects (DE) analysis, the response is held fixed for all other predictor variables outside of the predictor under examination to measure the effect of the stressor or management effectiveness in isolation from changes with confounders. Both TE and DE were done here, but the focus for the present paper will be on DE for incorporating causal assumptions in the estimates. The DE analysis is useful for risk-based approaches to examine the functional relationship between variables because the TE analysis includes noncausal associations in its calculations. To consider the causal relationships that covary with changes in the predictor as intermediate effects between the predictor and the target variable only, a nonconfounder class was identified. For coastal development threat, the marine-based pollution and overfishing threats were designated as nonconfounders in calculating the SDE. For management effectiveness, overfishing was designated a nonconfounder for calculating the SDE. The analysis in the present article will focus on these uses of nonconfounder variables.
A TMA with soft evidence included was used to examine the functional relationships between the target and the other variables. The major focus of the TMA was on whether relationships are linear. A TMA can be used to check for nonlinear impacts by plotting the coral reef variables’ mean values against the independently varied deviations in the means of stressor and management effectiveness variables. Soft and hard evidence throughout the range of the predictor node’s distribution were used for calculating variations. Because the means of the predictors are varied from the lowest to the highest values, the MinxEnt method is used to determine the probability distribution for each corresponding mean value to minimize the distance with the previous predictor node distribution. For each predictor, categorical variables were given state values of 0, 1, and 2 for low, medium, and high states or 0 and 1 for two ordered states. Direct effects were used for associated changes between the target variable and other variables. For each of the constructed networks, DE TMA was run to examine the effects of threats and management effectiveness on the coral reef health endpoints. From this process, response functions between the target coral reef health endpoints and the other variables were developed. The nonconfounders were accounted for in the DE TMA functions, but graphs without considering nonconfounders are reported in the Supplemental Data for reference purposes.
A plotting analysis based on graphing sensitivity measures with the average prior value of the stressor variables was constructed globally and in different regions of the world. Plotting the SDE with the a priori mean values of the predictors provides a way of visually comparing and identifying the most negative and positive SDE values for coral indicators with the lower and higher intensities of the threats and management effectiveness globally and in the different regions. For example, a high SDE value with a low prior mean value of threat indicates greater potential future risks if the threat intensity increases. A low SDE value with a high prior mean threat value indicates a threat that may not have much of a direct impact on the coral indicator and so on. The graphs were based on individual predictors but included all the indicators for each region and the global data set to visually examine groupings and relationships between threat intensity at sampling sites and effects. All SDEs highlighted in the plotting analysis were noted if the values were based on relationships that were highly nonlinear, given that the SDE would not be a good measure in those cases. Supplemental Data File 2 includes plotting analysis results for other sensitivity measures, including MI, KLD, TE, STE, and DE (Supplemental Data Figures S1–S6).
The highest overall sensitivity measures were summarized for all the model relationships between coral reef indicators and threats on a global and regional basis. These measures included the information theory measures (MI, KLD) along with positive and negative values for TE and DE and standardized versions. All these measures were the highest values with anticipated directional relationship (e.g., increasing thermal stress increases bleaching) within the TE and DE measures. Measures were also used from the TMA curves, including the minimum and maximum mean values for the reef health indicator and percent difference and absolute difference between the minimum and maximum mean values of the TMA. The TMA measures were used without consideration of the directionality as an overall measure of the extent of the association between indicators and predictors. However, LiveCoral was the only indicator examined for the minimum mean values on the TMA curves and was not considered for the maximum mean values. Thus, minimum TMA values were the overall lowest mean values for the stressor relationships with LiveCoral. Management effectiveness examined only the top-ranking associations without consideration of directionality.
RESULTS
Model evaluation
The number of discretization thresholds ranged from 3 to 6 (Table 1). Most final networks had an optimized SC of 1 and non-log-transformed data. However, in some cases, modifying the SC or log-transforming the data prior to discretization created significant improvements from cross-validation tests or better represented the distribution of the endpoint with more thresholds. Two endpoints, one each for LiveCoral and PopBleach, had final models that came from where the SC for the internal precision was highest. One model from PopBleach (Middle East) was chosen based on the inflection point on the SC versus structure-to-target precision ratio curve. The SC of 1 was used exclusively for the ColBleach, DeadCoral, and LCI models. The only endpoint with a majority of models that were either transformed or had an SC different from 1 was LiveCoral with all data (global), Australia, Middle East, and Southeast Asia which have log-transformed models with SC of 1 and, for Australia, with the optimal internal precision. The only other final models with log transformation were ColBleach for the Atlantic and Australia.
Table 1.
Node characteristics and total precision for target node networks
| Node | Region | Discretization thresholds | Discretization | Description | Total precision (%) |
|---|---|---|---|---|---|
| ColBleach | All | ≤0, ≤0.145, ≤0.374, ≤0.68, >0.68 | R2-GenOpt*, SC of 1 | Maximum percent coral colony bleached | 68.02 |
| Atlantic | ≤0, ≤0.101, >0.101 | R2-GenOpt*, SC of 1, log transforma | 52.24 | ||
| Australia | ≤0, ≤0.056, >0.056 | R2-GenOpt*, SC of 1, log transforma | 56.25 | ||
| Indian Ocean | ≤0, ≤0.188, >0.188 | R2-GenOpt, SC of 1 | 81.37 | ||
| Middle East | ≤0, ≤0.138, >0.138 | R2-GenOpt, SC of 1 | 67.18 | ||
| Pacific | ≤0, ≤0.291, ≤0.7, >0.7 | R2-GenOpt*, SC of 1 | 71.39 | ||
| Southeast Asia | ≤0, ≤0.119, ≤0.301, ≤0.595, >0.595 | R2-GenOpt*, SC of 1 | 80.04 | ||
| DeadCoral | All | ≤0, ≤0.075, ≤0.212, ≤0.45, >0.45 | R2-GenOpt*, SC of 1 | Maximum percent recently killed coral cover detected | 43.49 |
| Atlantic | ≤0, ≤0.069, ≤0.194, >0.194 | R2-GenOpt*, SC of 1 | 50.7 | ||
| Australia | ≤0, ≤0.144, >0.144 | R2-GenOpt, SC of 1 | 66.46 | ||
| Indian Ocean | ≤0, ≤0.219, >0.219 | R2-GenOpt, SC of 1 | 49.51 | ||
| Middle East | ≤0, ≤0.144, >0.144 | R2-GenOpt, SC of 1 | 41.35 | ||
| Pacific | ≤0, ≤0.263, >0.263 | R2-GenOpt, SC of 1 | 51.92 | ||
| Southeast Asia | ≤0, ≤0.125, ≤0.375, >0.375 | R2-GenOpt*, SC of 1 | 53.2 | ||
| LCI | All | ≤0, ≤0.118, ≤0.33, ≤0.683, >0.683 | R2-GenOpt*, SC of 1 | Reef health index calculated as the mean fraction live coral cover (live coral cover divided by the sum of recently killed cover plus live coral cover) | 40.21 |
| Atlantic | ≤0, ≤0.222, ≤0.571, >0.571 | R2-GenOpt*, SC of 1 | 49.65 | ||
| Australia | ≤0, ≤0.26, >0.26 | R2-GenOpt, SC of 1 | 66.46 | ||
| Indian Ocean | ≤0, ≤0.363, >0.363 | R2-GenOpt, SC of 1 | 50 | ||
| Middle East | ≤0, ≤0.243, >0.243 | R2-GenOpt, SC of 1 | 42.11 | ||
| Pacific | ≤0, ≤0.143, ≤0.396, >0.396 | R2-GenOpt*, SC of 1 | 47.6 | ||
| Southeast Asia | ≤0, ≤0.163, ≤0.468, >0.468 | R2-GenOpt*, SC of 1 | 50.79 | ||
| LiveCoral | All | ≤0, ≤0.04, ≤0.122, ≤0.241, ≤0.417, >0.417 | R2-GenOpt*, SC of 1, log transforma | Mean percent live coral cover | 30.92 |
| Atlantic | ≤0.122, ≤0.232, ≤0.369, >0.369 | R2-GenOpt*, SC of 1 | 40.67 | ||
| Australia | ≤0, ≤0.056, ≤0.263, >0.263 | R2-GenOpt*, SC based on internal precisionb, log transforma | 71.43 | ||
| Indian Ocean | ≤0.264, ≤0.486, >0.486 | R2-GenOpt*, SC of 1 | 44.12 | ||
| Middle East | ≤0, ≤0.088, ≤0.297, >0.297 | R2-GenOpt*, SC of 1, log transforma | 53.38 | ||
| Pacific | ≤0.284, ≤0.525, >0.525 | R2-GenOpt*, SC of 1 | 45.43 | ||
| Southeast Asia | ≤0, ≤0.05, ≤0.145, ≤0.286, ≤0.472, >0.472 | R2-GenOpt*, SC of 1, log transforma | 33.05 | ||
| PopBleach | All | ≤0, ≤0.086, ≤0.265, ≤0.507, >0.507 | R2-GenOpt*, SC of 1 | Maximum percent coral population bleached | 66.23 |
| Atlantic | ≤0, ≤0.316, >0.316 | R2-GenOpt, SC of 1 | 53.41 | ||
| Australia | ≤0, ≤0.1, >0.1 | R2-GenOpt, SC based on internal precisionb | 57.5 | ||
| Indian Ocean | ≤0, ≤0.135, >0.135 | R2-GenOpt*, SC of 1 | 79.41 | ||
| Middle East | ≤0, ≤0.067, >0.067 | R2-GenOpt, SC based on inflection pointb | 73.28 | ||
| Pacific | ≤0, ≤0.2, >0.2 | R2-GenOpt, SC of 1 | 66.11 | ||
| Southeast Asia | ≤0, ≤0.092, ≤0.278, >0.278 | R2-GenOpt*, SC of 1 | 76.45 | ||
| TNoB | None, severe | NA | Thermal stress based on extreme temperature events from 1998 to 2007 without accounting for bleaching | ||
| TB | None, severe | NA | Thermal stress based on extreme temperature and bleaching events from 1998 to 2007 with accounting for bleaching | ||
| Arag | Low, high for aragonite saturation states of >3.25 for low and 0–3.25 for high | Based on WRI Reefs at Risk classification for low, medium, and high acidification threat with medium and high combined (Cao and Caldeira 2008; Burke et al. 2011) | Acidification threat based on aragonite saturation. The layer assumes atmospheric CO2 is stabilized at 380 ppm for levels at time period under study | ||
| ME | — | Ineff_Unk_No, PartiallyEff, Effective | NA | Management effectiveness | |
| CDT | — | Low, Medium, High | NA | Coastal development threat from WRI’s Reefs at Riskc | |
| MBP | — | Low, medium, high | NA | Marine-based pollution threat from WRI’s Reefs at Risk | |
| WBP | — | Low, medium, high | NA | Watershed-based pollution threat from WRI’s Reefs at Risk | |
| OFadj | — | Low, medium, high | NA | Overfishing threat from WRI’s Reefs at Risk with adjustment by management effectiveness |
Arag = acidification threat; CDT = coastal development threat; ColBleach = colony bleaching endpoint; DeadCoral = recently killed coral endpoint; Effective = effective management; Ineff_Unk_No = ineffective or unknown or no management; LCI = live coral index; LiveCoral = live coral endpoint; ME=management effectiveness; OFadj = overfishing threat; PartiallyEff = partially effective management; PopBleach = population bleaching endpoint; SC = structural coefficient; TB = thermal stress with accounting for bleaching; TNoB = thermal stress without accounting for bleaching; WBP = watershed‐based pollution; WRI =World Resources Institute.
Log‐transformed data prior to discretization.
SCs used that are different from 1.
Total precision for the candidate models for each endpoint and region grouping ranged from 29% to 81% from the 10-fold cross validation analysis (Figure A2 in Supplemental Data File 1). A total of 174 candidate models were constructed with varying SCs and compared for precision with at least 4 models constructed for each region and endpoint and at most 6 candidate models if multiple SCs were used when the internal precision peaks and inflection points differed. The bleaching endpoints and live and dead coral endpoints tended to cluster around similar values and have similar ranges, although LiveCoral and PopBleach had the highest absolute ranges. The bleaching endpoints tended to have higher precisions, with most of the bleaching networks having greater than 50% precision. Less than half of most tested networks from other endpoints had greater than 50% precision. Three LiveCoral models exceeded 50%, and this endpoint had the fewest over 50%. Only PopBleach or ColBleach candidate models exceeded 70% total precision. Most models above 60% total precision were bleaching related but also included DeadCoral, LCI, and LiveCoral models for Australia. These can be visualized as the top outlying groupings of total precision values for the latter 3 indicators in Supplemental Data Figure A2. In some cases, log transformation significantly improved the models from less than to more than 50% total precision. This was seen for LiveCoral for the Middle East and for ColBleach for Australia. For LiveCoral in Australia, the total precision increased from 46% to 71% from log transformation and utilizing an SC lower than 1. The lowest grouping of total precision values for ColBleach were for nontransformed data in the Atlantic and Australia, and these values were improved above 50% through log transformation (Supplemental Data Figure A2). On the other hand, the lowest 2 values for PopBleach were from models built with log-transformed data for Australia, but the final model for these values was 57.5% total precision with nontransformed data (Supplemental Data Figure A2). Supplemental Data File 2 contains all numerical total precision values for the candidate models, including those that were not selected (Table S1).
Relationship analysis with the target nodes
Thirty-five final networks were used and their capabilities for predicting levels of the coral reef indicators were evaluated with several model-based measures described in Methods. All numerical sensitivity values for relationships between the target coral reef indicator and the predictors are in Supplemental Data File 2 (Tables S2–S17). The prior mean values of the nodes for the threat variables and management effectiveness are also in the Supplemental Data, along with graphs for TMA curves and statistics relating to maximum and minimum values of the curves. The results below focus on MI and SDE statistics. These are the most relevant statistics, MI for summarizing model sensitivity and SDE for the strength of relationships with coral indicators. A summary of the highest numerical values for all of the relationship measures on a regional basis are provided at the end of the results.
Mutual information.
The MI statistics provide a nonlinear measure of sensitivity for relationships by quantifying the amount of uncertainty reduced on a node by conditioning on another node. Depicting the MI values on the arcs of a network can help visualize how this relationship works (Figure 2). The MI values are symmetric and provide a useful bidirectional measure of sensitivity through uncertainty reduction. Stronger relationships among predictors can be identified in augmented naïve models and this can be seen, for example, with the relationships between management effectiveness and overfishing as well as between overfishing and coastal development threat. Coastal development threat and marine-based pollution along with overfishing and watershed-based pollution also had stronger relationships than any of the predictors with the target node in the Atlantic model. The strongest relationship of ultimate interest is with LCI and watershed-based pollution, with LCI and overfishing threat being the only target node relationship that is not more than half of the MI for LCI and watershed-based pollution. Additional highlights from target node (coral reef indicator) relationships with predictors were compared and extracted across the models for MI and discussed in the Relationship analysis measures section below. The amount of uncertainty reduced can be presented through a percent value that will differ between the directions due to the prior distributions.
Figure 2.
Mutual information statistics (numbers in boxes) for the LCI network for Atlantic data. Black numbers represent the mutual information which is symmetric in both directions of the arc. Blue and red numbers represent the percent reduction in uncertainty in the forward and reverse directions of the arc, respectively. Line weights are the relative magnitude of mutual information between 2 nodes in comparison with all of the other arcs’ mutual information values. Arag = acidification threat; CDT = coastal development threat; LCI = live coral index; MBP = marine-based pollution; ME = management effectiveness; OFadj = overfishing and destructive fishing threat; TB = thermal stress; WBP = watershed-based pollution.
The relationships of ultimate concern are between the coral indicators and the predictors and not among the predictors themselves. The MI measures are used in a relative sense to depict the strongest overall relationships between coral indicators and predictors for each of the regions. Most of the coral indicator relationships with higher MI values were in Australia. The top 7 MIs were in Australia as well as 12 of the top 20 highest MI values. The highest MIs were for Australia and DeadCoral with acidification threat and management effectiveness and LCI with management effectiveness and acidification, respectively. The highest overall MI for the Middle East and Australia was between DeadCoral and acidification threat. For Southeast Asia, it was also acidification threat but with LiveCoral. The greater sensitivity with acidification threat and the indicators was a common theme across multiple measures in Supplemental Data File 2 (Tables S2–S17). For the Atlantic, the highest MI was between watershed-based pollution and LiveCoral. The Indian Ocean had the only relationship that was highest for management effectiveness (with ColBleach). Like the Middle East and Australia, the Pacific also had the highest MI for DeadCoral but with a local threat (overfishing).
Standardized direct effects.
The TMA with direct effects will be discussed in the next section but decidedly nonlinear relationships will be highlighted when identifying patterns with the SDE. The SDE values from all 35 networks are discussed within the context of SDE versus stressor mean value plots.
Plotting SDE values with prior mean values of stressors provides a way to judge potential future associations of the predictors and indicators (Figure 3). These prior mean plots provide a way of looking at the magnitude of the relationship between threats and coral reef indicators along with the expected values of the predictors. The positive SDE values can indicate increasing risks as the stressor increases with a negative outcome such as DeadCoral or bleaching. The lower SDE values were also of interest for indicating a strongly negative linear relationship with living coral and stressors. The opposite relationships are expected with management effectiveness and coral indicators from the stressors. Target mean analysis using DE was used to test whether relationships were linear before ranking and comparing. Relationships that were concave, convex, or had threshold changes were deemed not representative of the SDE value. Some relationships were not completely linear but close enough to be accepted as adequate. In some of the nonlinear cases, the SDE value was taken at a location on the curve that did not represent the slope of most of the curve or of major features in the relationship between the variables from the TMA. Whenever highest or lowest SDE associations are mentioned, any that have a significantly nonlinear relationship are highlighted.
Figure 3.
Standardized direct effects and stressor prior mean value plots for Arag (acidification threat) (A); CDT (coastal development threat) (B); MBP (marine-based pollution) (C); ME (management effectiveness) (D); OF (overfishing and destructive fishing threat) (E); TS (thermal stress) (F); and WBP (watershed-based pollution) (G). For the gray shaped plot points, ColBleach = colony bleaching endpoint; DeadCoral = recently killed coral endpoint; LCI = live coral index; LiveCoral = live coral endpoint; PopBleach = population bleaching endpoint. For the colored circles in the legend, All = all data; Atl = Atlantic data; Aus = Australia data; IO = Indian Ocean data; ME = Middle East data; Pac = Pacific data; SEA = Southeast Asia data.
The highest (positive) and lowest (negative) SDE associations can be visualized and identified in the prior mean plots (Figure 3). The highest positive SDE was between DeadCoral and management effectiveness in Australia. The second highest was between DeadCoral and acidification threat in the Middle East. The management effectiveness relationship was not in the expected direction (i.e., increasing effectiveness was positively associated with DeadCoral) but the acidification relationship was in the expected direction (i.e., increased acidification threat was associated with higher DeadCoral). However, acidification threat should be interpreted with caution in the Middle East due to 88% of the data being extrapolated from adjacent water bodies. In contrast, 1.2% of the Atlantic, 44% of Australia, 9.3% of the Indian Ocean, 1.7% of the Pacific, and 31% of Southeast Asia were extrapolated. The lowest SDE was also for acidification threat but for DeadCoral in Australia. The second lowest was for LiveCoral and overfishing threat in Australia. The latter was in the expected direction with increasing stressor being inversely associated with LiveCoral. Across all SDE plots, Australia tended to have lower threat levels for different indicator relationships as seen for coastal development threat, overfishing, thermal stress, and bleaching endpoints and watershed-based pollution. But the SDE values indicated higher linear sensitivities for Australia with ColBleach, PopBleach, and LiveCoral. Australia also had the highest management effectiveness prior mean value.
Other acidification SDEs were relatively higher in the Middle East, Southeast Asia, and Australia (Figure 3A). Australia had the highest mean value for acidification threat and had the lowest overall negative SDE value for acidification threat and DeadCoral. The latter was also the highest overall MI value. For Australia, the highest SDE was for ColBleach and acidification threat, which was the second overall highest SDE for acidification threat. The Middle East had the only negative LiveCoral value, which was in the expected direction (decreasing LiveCoral associated with increasing acidification threat). On the other hand, Southeast Asia mostly had negative SDE values, with acidification threat and LiveCoral being the 1 positive value. For Southeast Asia, acidification threat and LiveCoral had the highest SDE and this relationship also has the highest MI and KLD.
In Southeast Asia the lowest (negative) SDE value was for LiveCoral and CDT. Coastal development threat was highest in Southeast Asia (Figure 3B), indicating that LiveCoral were facing higher exposure to stressors and risks from coastal development during the time period of the monitoring. Australia and the Middle East also had negative SDE values for LiveCoral and CDT, with Australia having the lowest mean value. The CDT had higher positive SDE values with PopBleach in Australia and in the Indian Ocean, and was highest with LCI in the Pacific. However, the relationship between CDT and LCI in the Pacific had a concave downward shape at the end of the TMA curve, indicating decreasing LCI values after the sharp increase. Although Southeast Asia had the highest mean value for CDT, the SDEs were generally lower in that region. The DE relationships tended to be nonlinear for Southeast Asia and CDT.
Marine-based pollution had the highest positive SDE value for LCI in the Middle East and the second highest marine-based pollution mean value (Figure 3C). The most negative SDE values for marine-based pollution were found for LiveCoral in the Middle East and Southeast Asia. For lower marine-based pollution mean values, the Indian Ocean had a low SDE positive value for PopBleach, and the DE curve was practically flat. However, Southeast Asia had one of the higher SDE values for LCI and one of the lowest for LiveCoral, indicating a potential for future risks for that region and coral health.
More than half of the management effectiveness relationships had negative SDE values (Figure 3D). All indicators are expected to have negative associations with increased management effectiveness except for LiveCoral, which is expected to be positive. The highest and lowest SDE values for management effectiveness were not in the expected direction of association. The prior mean value for management effectiveness was highest in Australia, suggesting there is more management effectiveness in that region. The highest SDE for management effectiveness was for DeadCoral in Australia. The relationship between DeadCoral and management effectiveness was largely linear but had a slight decrease at higher values of management effectiveness. In the Middle East, LiveCoral had the lowest (negative) SDE for management effectiveness. In Australia, the SDE value for LiveCoral was relatively high and positive with management effectiveness, but the relationship was nonlinear. For the Pacific, DeadCoral had among the lowest SDE values with management effectiveness; however, the TMA curve had a slight increase for DeadCoral with higher mean values of management effectiveness.
Overfishing had strong relationships based on SDE values. The lowest negative SDE was between LiveCoral and overfishing in Australia (Figure 3E). The ColBleach indicator was among the most positive for Australia and overfishing, but this relationship was nonlinear and had a strong decreasing component to the curve. Australia had the lowest mean overfishing value of all the regions. LiveCoral also had a negative SDE for overfishing in Southeast Asia. Southeast Asia had the highest mean value for overfishing threat. The Pacific had the most positive SDE value for overfishing for DeadCoral, but PopBleach and LCI were also among the higher values—the highest overall SDE in the Pacific was for overfishing and DeadCoral, with LCI and PopBleach being second and third. The Pacific had the second lowest mean value for overfishing. For the Atlantic, the lowest negative SDE for overfishing was for ColBleach, which was not the expected directionality. Outside of the Atlantic, most relationships for DE were nonlinear, but negative SDE values with overfishing were observed for ColBleach for all regions but the Pacific, Australia, and the Middle East.
Australia had the lowest thermal stress mean value for the bleaching indicators. However, the Indian Ocean had the second lowest thermal stress mean value and the highest SDE for DeadCoral, both for thermal stress and for any stressor–SDE relationship for the region (Figure 3F). For the Atlantic, the highest positive SDE was for ColBleach and thermal stress. As expected, LiveCoral values were mostly negative and had the lowest (negative) SDE values for thermal stress in Australia, the Middle East, and globally (all data). For Australia and all data, the relationships were nonlinear. For the Pacific, the most negative overall SDE values were for DeadCoral and LiveCoral with thermal stress. The former was not the expected directionality. The most negative overall SDE value in the Middle East was for LiveCoral and thermal stress.
The highest SDE values for watershed-based pollution were for ColBleach and PopBleach in the Middle East, the expected directionality for both (Figure 3G). The Middle East, along with Australia, had the lowest prior mean value for watershed-based pollution, indicating a potential future risk for that region. The bleaching indicators in the Atlantic were among the highest positive SDE values, but ColBleach had a concave downward functional relationship with watershed-based pollution threat. LiveCoral had some of the lowest negative SDE values for watershed-based pollution threat in Australia, the Indian Ocean, and the Atlantic. The lowest SDE for watershed-based pollution threat was in the Indian Ocean with LiveCoral. The most negative overall SDE for the Atlantic was for watershed-based pollution threat and LiveCoral. The latter had a sigmoidal relationship between the LiveCoral mean value and watershed-based pollution from the DE TMA function.
Target mean analysis with direct effects.
The DE TMA constructed response curves that relate each of the predictors (threats and management effectiveness) to the coral reef indicator variables. From these curves, nonlinearities in relationships and positive and negative directionality throughout multiple points of the relationships can be examined. The DE TMA uses the model to allow other variables to covary and therefore is a useful means to assess associations with the model given the relationships that were identified by the machine learning algorithms. The TMA curves were derived from the final Bayesian networks chosen in the validation stage. Each of the DE TMA curves, along with TMA curves constructed with total effects, are provided in Supplemental Data File 2 (Figures S7–S109). However, 3 example DE TMA curves are reviewed here (Figures 4–6). Supplemental Data File 2 figures contain DE TMA plots with and without nonconfounders considered for management effectiveness and coastal development threat. These raw direct effect calculations give a picture of the variable-to-variable relationships, but the nonconfounders are used for both predictors here as a more accurate calculation of the direct effects if causality can be inferred from the data.
Figure 4.
Direct effects of stressors and management effectiveness variables on colony bleaching (ColBleach) mean values for the Pacific. The predictors in the legend are ordered from positive to negative based on their raw direct effect scores calculated from the derivative of the prior mean values of the variables.
Figure 6.
Direct effects of stressors and management effectiveness variables on recently killed coral (DeadCoral) mean values for the Pacific. The predictors in the legend are ordered from positive to negative based on their raw direct effect scores calculated from the derivative of the prior mean values of the variables.
The DE TMA for ColBleach in the Pacific indicated a flat relationship between the mean of ColBleach from changes throughout the range of the distribution of all 7 predictors (Figure 4). However, at higher levels of overfishing, an increase in the mean value of ColBleach was observed. The opposite phenomenon occurs for higher levels of management effectiveness, where increases to management effectiveness were strongly associated with decreases to the ColBleach mean. This happened after an initially flat relationship that steadily decreased as management effectiveness increased. Overfishing was permitted to also change with changes to the management effectiveness distribution, whereas other distributions were held fixed at their initial (prior) levels. The difficulty with relying on linear coefficients such as SDE alone can clearly be seen from these nonlinear relationships.
Of all the indicators, the proportion of LiveCoral is one of the most important for measuring the health of the reef. Most management effectiveness standardized direct effect relationships with LiveCoral were not interpretable and in counterintuitive directions. One exception was for the LiveCoral model in Southeast Asia (Figure 5). Here we see a curvilinear increase in LiveCoral mean values from changes to management effectiveness from ineffective to effective. A steady decrease in LiveCoral was also observed from increases in overfishing threat, and the 2 lines cross close to when the middle state is fully conditioned on for each of the distributions. Coastal development threat, marine-based pollution, and thermal stress were also associated with decreases in LiveCoral cover. Marine-based pollution was the highest risk stressor in this example by the lowest point of the curve (lowest LiveCoral mean value) and directionality influences on LiveCoral. Other stressors (i.e., acidification threat and watershed-based pollution threat) were in counterintuitive directions with changes to LiveCoral.
Figure 5.
Direct effects of stressors and management effectiveness variables on live coral cover (LiveCoral) mean values for Southeast Asia. The predictors in the legend are ordered from positive to negative based on their raw direct effect scores calculated from the derivative of the prior mean values of the variables.
Another interesting example of a DE TMA is for DeadCoral in the Pacific (Figure 6). For this model, most of the stressors had counterintuitive relationships with DeadCoral except for overfishing threat, marine-based pollution, and acidification threat. Coastal development threat had a concave downward relationship so that lower values were associated with higher DeadCoral and higher values of coastal development threat had the opposite relationship. Management effectiveness had a convex direct effect, reducing DeadCoral as the distribution transitioned from ineffective to partially effective management states. This tapers off with increases from partially effective to effective management and, for the higher end of the curve, is even associated with slight increases in the DeadCoral mean values. Watershed-based pollution threat had a fully linear DE relationship with DeadCoral but in a counterintuitive direction, with decreasing DeadCoral at higher levels.
The DE TMA curves are useful visual tools built from nonparametric relationships between distributions and do not have “natural” statistics. However, summarizing the high and low values can provide information on the relationships. The highest DE TMA mean value for a bleaching or DeadCoral endpoint due to stressors was ColBleach and marine-based pollution in Australia. The lowest minimum mean DE TMA values for LiveCoral were for the Atlantic and each stressor (watershed-based pollution, overfishing, marine-based pollution, coastal development threat, acidification threat, and thermal stress, from lowest to highest minimum mean LiveCoral values, respectively). After all of the Atlantic stressors, the next lowest minimum mean DE TMA LiveCoral value was for overfishing in Australia and for marine-based pollution in Southeast Asia. Across all of the stressors, the highest bleaching means from the DE TMA were for ColBleach in Australia and the Atlantic. For the Atlantic, the overall highest percent difference between the highest and lowest mean values across the DE TMA curves was found for marine-based pollution threat and DeadCoral. For the Pacific, the highest percent difference was for PopBleach and overfishing threat and for Southeast Asia, the highest was for LCI and acidification threat. In Australia, the highest percent difference was also found for overfishing and DeadCoral. For the Middle East, it was PopBleach and watershed-based pollution. For the Indian Ocean, the highest percent difference was found for PopBleach and acidification threat, which was the highest percent difference overall.
Relationship analysis measures.
The sensitivity analysis measures for all relationships between coral reef indicators and stressors or management effectiveness provide one way of interpreting the relationships in the models. Examining the top relationships between coral reef endpoints and stressors (Table 2) or management effectiveness (Table 3) for different regions can help identify endpoints and stressors that are tightly coupled and what is most useful to monitor. The TE, DE, STE, and SDE statistics are linear measures but the others are not. The LiveCoral values were always selected for the negative linear relationships or minimum mean values for DE or TE curves. However, LiveCoral was frequently found in the highest ranked TMA values, especially for the Atlantic and Australia. Acidification threat for the Middle East was not considered in the rankings due to the high percentage of missing data from limited coverage of the aragonite saturation layer in the Middle East.
Table 2.
Top stressor–endpoint relationships for different measures and regions
| Measure | AllData | Atlantic | Australia | Indian Ocean | Middle East | Pacific | Southeast Asia |
|---|---|---|---|---|---|---|---|
| Mutual information | ColBleach-Arag | LiveCoral-WBP | LiveCoral-OF | PopBleach-CDT | LCI-MBP | DeadCoral-OF | LiveCoral-TS |
| Kullback-Leibler divergence | ColBleach-Arag | CoBleach-Arag | LiveCoral-TS | LiveCoral-WBP | PopBleach-MBP | DeadCoral-OF | LCI-WBP |
| Direct effects (most negative) | LiveCoral-MBP | LiveCoral-WBP | LiveCoral-OF | LiveCoral-WBP | LiveCoral-TS | LiveCoral-TS | LiveCoral-MBP |
| Direct effects (most positive) | ColBleach-Arag | ColBleach-Arag | ColBleach-Arag | LCI-Arag | LCI-MBP | PopBleach-Arag | LCI-MBP |
| Standardized direct effects (most negative) | LiveCoral-TS | LiveCoral-WBP | LiveCoral-OF | LiveCoral-WBP | LiveCoral-TS | LiveCoral-TS | LiveCoral-CDT |
| Standardized direct effects (most positive) | ColBleach-Arag | ColBleach-Arag | ColBleach-Arag | DeadCoral-TS | PopBleach-WBP | DeadCoral-OF | LCI-MBP |
| Total effects (most negative) | LiveCoral-TS | LiveCoral-WBP | LiveCoral-TS | LiveCoral-WBP | LiveCoral-TS | LiveCoral-TS | LiveCoral-TS |
| Total effects (most positive) | ColBleach-Arag | ColBleach-Arag | ColBleach-Arag | LCI-Arag | LCI-MBP | PopBleach-Arag | LCI-WBP |
| Standardized total effects (most negative) | LiveCoral-TS | LiveCoral-WBP | LiveCoral-OF | LiveCoral-WBP | LiveCoral-TS | LiveCoral-TS | LiveCoral-CDT |
| Standardized total effects (most positive) | ColBleach-Arag | ColBleach-Arag | ColBleach-Arag | ColBleach-TS | PopBleach-WBP | DeadCoral-OF | LCI-WBP |
| Target mean analysis direct effects (absolute numerical difference) | LiveCoral-MBP | LCI-WBP | LiveCoral-OF | LCI-Arag | LiveCoral-TS | ColBleach-OF | LiveCoral-MBP |
| Target mean analysis direct effects (% difference) | PopBleach-OF | DeadCoral-MBP | DeadCoral-OF | PopBleach-Arag | PopBleach-WBP | PopBleach-OF | LCI-Arag |
| Target mean analysis direct effects (maximum) | LCI-MBP | LCI-WBP | ColBleach-MBP | LCI-Arag | LCI-MBP | ColBleach-OF | LCI-MBP |
| Target mean analysis direct effects (minimum) | LiveCoral-MBP | LiveCoral-WBP | LiveCoral-OF | LiveCoral-WBP | LiveCoral-MBP | LiveCoral-MBP | LiveCoral-MBP |
| Target mean analysis total effects (absolute numerical differences) | ColBleach-Arag | LiveCoral-MBP | LiveCoral-OF | LCI-Arag | LCI-MBP | LCI-OF | LiveCoral-Arag |
| Target mean analysis total effects (% difference) | ColBleach-Arag | LiveCoral-Arag | DeadCoral-OF | PopBleach-Arag | PopBleach-WBP | PopBleach-Arag | ColBleach-MBP |
| Target mean analysis total effects (maximum) | ColBleach-Arag | ColBleach-Arag | ColBleach-MBP | LCI-Arag | LCI-MBP | LCI-OF | LCI-WBP |
| Target mean analysis total effects (minimum) | LiveCoral-MBP | LiveCoral-Arag | LiveCoral-OF | LiveCoral-WBP | LiveCoral-MBP | LiveCoral-MBP | LiveCoral-CDT |
Arag = acidification threat; CDT = coastal development threat; ColBleach = colony bleaching; DeadCoral = dead coral; LCI = live coral index; LiveCoral = live coral; MBP = marine‐based pollution threat; OF = overfishing threat; PopBleach = population bleaching; TS = thermal stress; WBP = watershed‐based pollution.
Table 3.
Top management effectiveness–endpoint relationships for different measures and regions
| Measure | AllData | Atlantic | Australia | Indian Ocean | Middle East | Pacific | Southeast Asia |
|---|---|---|---|---|---|---|---|
| Mutual information | ColBleach | ColBleach | LCI | ColBleach | LiveCoral | DeadCoral | DeadCoral |
| Kullback-Leibler divergence | ColBleach | ColBleach | LCI | ColBleach | LiveCoral | DeadCoral | DeadCoral |
| Direct effects (most negative) | DeadCoral | PopBleach | No negative | LiveCoral | LiveCoral | LiveCoral | LCI |
| Direct effects (most positive) | ColBleach | LCI | DeadCoral | ColBleach | LCI | No positive | LiveCoral |
| Standardized direct effects (most negative) | DeadCoral | PopBleach | No negative | LiveCoral | LiveCoral | DeadCoral | DeadCoral |
| Standardized direct effects (most positive) | ColBleach | LCI | DeadCoral | ColBleach | LCI | No positive | LiveCoral |
| Total effects (most negative) | DeadCoral | PopBleach | LCI | LiveCoral | LiveCoral | LiveCoral | LCI |
| Total effects (most positive) | ColBleach | LCI | LiveCoral | ColBleach | LCI | ColBleach | LiveCoral |
| Standardized total effects (most negative) | DeadCoral | PopBleach | LCI | LiveCoral | LiveCoral | DeadCoral | LCI |
| Standardized total effects (most positive) | ColBleach | LCI | LiveCoral | ColBleach | LCI | ColBleach | LiveCoral |
| Target mean analysis direct effects (absolute numerical difference) | ColBleach | LCI | ColBleach | LiveCoral | LCI | LiveCoral | DeadCoral |
| Target mean analysis direct effects (% difference) | ColBleach | LCI | PopBleach | ColBleach | LCI | ColBleach | DeadCoral |
| Target mean analysis direct effects (maximum) | LiveCoral | ColBleach | LiveCoral | LiveCoral | LiveCoral | LiveCoral | LiveCoral |
| Target mean analysis direct effects (minimum) | PopBleach | DeadCoral | PopBleach | PopBleach | PopBleach | PopBleach | PopBleach |
| Target mean analysis total effects (absolute numerical differences) | ColBleach | LiveCoral | LiveCoral | LiveCoral | LCI | ColBleach | DeadCoral |
| Target mean analysis total effects (% difference) | ColBleach | PopBleach | PopBleach | ColBleach | LCI | ColBleach | DeadCoral |
| Target mean analysis total effects U | LiveCoral | LiveCoral | LiveCoral | LiveCoral | LCI | LiveCoral | LiveCoral |
| Target mean analysis total effects (minimum) | PopBleach | DeadCoral | PopBleach | PopBleach | PopBleach | PopBleach | PopBleach |
ColBleach = colony bleaching; DeadCoral = dead coral; LCI = live coral index; LiveCoral = live coral; MBP = marine‐based pollution threat; PopBleach = population bleaching.
The all data, Atlantic, and Australia partitions were dominated by ColBleach relationships with stressors. For these regions, acidification threat and ColBleach were frequently tightly related. For the Indian Ocean, acidification threat was highly associated with LCI for multiple measures. For all data, the strongest negative TE–DE and minimum TMA relationships for LiveCoral were with thermal stress and marine-based pollution. Population bleaching and LCI also made single appearances in the TMA rankings for all data with overfishing and marine-based pollution, respectively. The LCI–marine-based pollution relationship was seen in the Middle East and Southeast Asia and the PopBleach–overfishing relationship was seen in the Pacific for the same measures. For the Atlantic, LiveCoral was most often connected to watershed-based pollution. This relationship was also observed for the Indian Ocean. The overfishing and destructive fishing threat and LiveCoral relationship was dominant in Australia. For the Indian Ocean, Middle East, and Pacific, LCI and PopBleach became more dominant. The LCI values were especially sensitive in Southeast Asia. For the Middle East and Southeast Asia, marine-based pollution gained in importance and was often found with LCI and LiveCoral. Watershed-based pollution and LiveCoral were seen together only in the Atlantic and Indian Ocean. Thermal stress appeared the most in the Middle East with LiveCoral followed by the Pacific. The DeadCoral relationships were only found in more than 2 top association measure rankings in the Pacific (Table 2).
For management effectiveness, stronger relationships were frequently found with ColBleach in all data, Indian Ocean, and the Pacific data partitions (Table 3). For the global models, management effectiveness was most highly associated with ColBleach overall, DeadCoral with the linear measures, LiveCoral for maximum TMA values, and PopBleach for minimum TMA values. Across all regions, minimum mean TMA values were also most often found for PopBleach, and maximum values were most often found for LiveCoral. Management effectiveness was frequently related to LCI in the Atlantic and Middle East and to LiveCoral in Australia, the Indian Ocean, the Middle East, the Pacific, and Southeast Asia. The TMA absolute and percent differences for TE and DE curves were often the same except when LiveCoral was the highest absolute difference. In those cases, one of the bleaching measures had the highest percent difference. However, some regional differences can be discerned. For the Middle East, LCI and LiveCoral were dominant, and DeadCoral and ColBleach were not in the top rankings. In the Indian Ocean, LiveCoral and ColBleach were dominant, and there were no DeadCoral or LCI relationships in the top rankings. For the Atlantic and Australia, PopBleach appeared more often in the top rankings for the measures. For the Atlantic, PopBleach was more often highly ranked with management effectiveness than any other region. For Southeast Asia, DeadCoral was the most responsive to management effectiveness, and ColBleach was not in the top rankings.
DISCUSSION
Coral reefs provide a wealth of ecosystem services to humans but are facing multiple anthropogenic threats from local to global sources. A global analysis of human impacts on the oceans found that half of the coral reef systems were experiencing medium to high impacts from stressors (Halpern et al. 2008). To examine the relationship of stressor intensity to indicators of coral reef health, BNs were used for screening risks from global data sets and to examine sensitivity with direct effects. The BNs provided powerful insights for examining the overlap between stressors and resource condition data. In bringing together spatial data sets for building predictive models, the BNs offered capabilities for handling missing data and for handling colinear and nonlinear relationships among independent variables (Pawson et al. 2017). This situation would have presented an enormous challenge for conventional approaches but was easily handled by the BNs. As stated by Aven (2013), “Data itself [are] of no value until [they are] transformed into a relevant form.” The BN capabilities for predicting changes to coral health indicators from spatial threats and summarizing relationships in the models with meaningful measures facilitated understanding of risks and uncertainties. This, combined with the adaptability of BNs, provided potential methods for future risk assessments.
Associations among variables were examined through conditioning on the model predictors and examining changes to coral reef indicators through direct effects measures and graphical plots of relationships. Mutual information and KLD are information theory measures for sensitivity and should be preferred in most cases over correlation coefficients that require linearity between variables. Although these information theory measurements can provide ranges of sensitivity, they may not capture a consistent stressor–response relationship in terms of directionality of associations. Standardized direct effects measures provided greater clarity on stressor–response relationships, but their interpretation can be difficult for nonlinear relationships. A direct effects analysis was implemented by incorporating additional causal assumptions such as downstream causal variables (nonconfounders) and noncontrollable variables. Future work can use this approach for models built to inform management decision making (Conrady and Jouffe 2013), and for higher resolution fishing and physical damage variables that would be controlled by improved spatial management for reef resiliency.
Overall, the TMA curves indicated that the linear assumption was often adequate, but sometimes the TE, DE, and standardized indicators of total and direct effects were inaccurate. By far the majority of the nonlinear TMA curves were associated with DE graphs. There were approximately 3 times more nonlinear associations with the DE TMA curves than the TE TMA curves, potentially indicating greater noise in the data. The greater number of DE TMA curves that were not linear indicated that the probabilistic dependencies in the models tended to smooth out more of the direct noise in the data. Because global threats had only 2 states, there were more linear associations for the TMA curves. The DE TMA provided necessary information on the relationship between the variables, including the functional form of nonlinear relationships. The interpretation of the directional measures is affected by whether the relationships in the TMA are linear and may not be directly comparable across variables with different scales that must be normalized prior to comparisons. The TMA also provided information about the model relationships, including threshold points between positive and negative associations that are not captured in the single measures for evaluating sensitivity. Linear and nonlinear interactions were observable that are normally not seen in risk assessments, with or without BNs. Plotting prior means against sensitivity measurements is also known as a “multiquadrant analysis” and is useful in product development and optimization (Conrady and Jouffe 2015) but can be useful for environmental assessments as well. Taken together, the approaches described here can provide clarity on relationships in spatial databases of environmental stressors and condition, including the noise in the data and the strength of the models through cross-validation.
Focusing on risks to LiveCoral was important given the significance of LiveCoral as a reef indicator. Negative effects to LiveCoral have been associated with sewage pollution (Hodgson and Liebeler 2002), and this was found to be mostly the case here. The SDE measures for all regions had a negative association between LiveCoral and coastal development threat, except for the Atlantic and Indian Ocean. However, from the TMA curves, Australia had the strongest relationships between LiveCoral and coastal development threat. The world’s reefs experienced a major thermal stress event in 1998 that caused a 10% reduction in LiveCoral globally (Hodgson and Liebeler 2002). Thermal stress and LiveCoral were negatively correlated from SDE in all cases except for the Atlantic, which had a very weak to non-existent relationship to thermal stress. Live coral cover was negatively associated with blast fishing in Southeast Asia and to poison fishing in the Indo-Pacific in a Reef Check survey (Hodgson and Liebeler 2002). This aligns with results from the current analysis, where overfishing and destructive fishing threat was negatively correlated to LiveCoral in Southeast Asia. The highly negative correlation for the SDE for LiveCoral and overfishing in Australia was coupled with a relatively low average fishing threat to indicate a potential for future risk if overfishing increases.
Along with LiveCoral, ColBleach was also frequently found to be potentially at risk from multiple different stressors. In terms of magnitude and direction, the strongest and most frequent stressor with the greatest risks for ColBleach was acidification. For acidification, PopBleach was also a useful risk measure for some regions. Both bleaching indicators were generally susceptible to thermal stress. Thermal stress was a risk factor for ColBleach in the Indian Ocean. This is reflected in the 1998 temperature spike, which caused greater bleaching in the Indian Ocean than in other regions around the world (Burke et al. 2011). Likewise, PopBleach was positively associated with thermal stress in the Indian Ocean but had stronger positive associations with acidification.
Recently killed coral was related to destructive fishing and sewage pollution in Hodgson and Liebeler (2002). In the present assessment, DeadCoral was also frequently positively associated with overfishing threat in the Pacific, Southeast Asia, the Middle East, and the Indian Ocean for the DE and TE measures. However, many of these relationships were nonlinear, but all had an increasing relationship in at least part of the curve. Australia had a negative association between overfishing threat and DeadCoral. Coastal development threat and DeadCoral had negative associations for all measures except for direct effects measures in Australia and the Indian Ocean, but these relationships were nonlinear.
Hodgson and Liebeler (2002) noted a decrease in the LCI in the Indo-Pacific due to the 1997–1998 bleaching event that was largely driven by a rise in DeadCoral. The association with thermal stress and LCI in Southeast Asia and the Pacific was negative, which is the opposite of the expected directionality. This may reflect the use of average values of the LCI and the recovery that occurred in subsequent years. The Atlantic region was noted to not have a large change in the LCI across a 6-y survey (Hodgson and Liebeler 2002). For the difference in mean value changes from the DE and TE TMA analysis, the Atlantic had the lowest overall changes in percent difference and absolute mean values for LCI and acidification and thermal stress threats.
The prior mean values for global threats tended be higher for the Middle East. However, acidification values were largely extrapolated for adjacent water bodies such as the Indian Ocean and Mediterranean Sea for the Middle East reefs, and this made their estimates highly uncertain outside of the probabilities in the model. For local threats, the Atlantic tended to be at the higher end of the prior mean values and was the highest for coastal development threat and marine-based pollution. The WRI report that accompanied the threat GIS layers found that local stressors are most severe in Southeast Asia and least severe in Australia based on percent reefs threatened (Burke et al. 2011). For the sampled site data used here, Australia tended to have lower prior mean threat values for overfishing, watershed-based pollution, and coastal development threat than Southeast Asia (Figure 3). However, Australia had higher prior mean values for acidification threat and marine-based pollution. When comparing the indicator relationships for these 2 regions, there was not a clear dominant relationship based on the directional statistics alone. However, the low prior mean values for some stressors and higher sensitivity for coral reef endpoints in Australia indicated the potential for future changes associated with threats for this region.
A Reef Check global survey in the early phases of the time period covered by the data (1997–2001) found that overall anthropogenic impacts were higher in the Atlantic than in the Pacific (Hodgson and Liebeler 2002). Prior mean values for threats were higher for the Atlantic except for watershed-based pollution, which was higher in the Pacific.
Besides multiple stressor types, the relationship of the indicators with management effectiveness was also considered. For management effectiveness, DeadCoral indicators were most useful in terms of being predictable from direction of association with the stressors. For the Indian Ocean, regions with marine protected areas were found to have higher mortality after the 1998 bleaching event but showed faster recovery by the period 2001–2005 (Ateweberhan et al. 2011). In the current analysis, DeadCoral was negatively correlated with management effectiveness for all regions except the Atlantic and Australia, but most of the relationships were nonlinear from the DE TMA. Previously established marine protected areas were observed to increase coral cover from multidecadal coral surveys (1969–2006) over the long term (Selig and Bruno 2010). Coral cover was found to be “greater than expected” in the Indo-Pacific, with well-managed areas having similar coral cover to less well managed areas (Bruno and Selig 2007). In the present analysis, LiveCoral was a potentially useful indicator for management effectiveness in Southeast Asia along with the Atlantic. Higher SDE values for management effectiveness and LiveCoral were found for Australia, but the curve was highly nonlinear with a strong decreasing component.
From cross-validation statistics, greater confidence can be placed in some of the models, particularly PopBleach and ColBleach in Southeast Asia and the Indian Ocean, PopBleach in the Middle East, ColBleach in the Pacific, and LiveCoral in Australia. The lowest total precisions were found for LiveCoral for all data and Southeast Asia and LCI for all data. The bleaching indicator models generally, but not always, performed better than the other endpoints. Log-transforming emphasized areas of the distribution and, in several cases, was found to significantly improve the validation of the variables. This suggests log-transforming should be considered with untransformed data as well. Discretization can impact the interpretation of continuous coral reef indicator variables. The R2-GenOpt* algorithm provided a powerful tool for identifying useful break points for a distribution and intervals that ensure data coverage while representing the marginal distributions of the indicators. Modifying the SC values did not always improve out-of-sample validation statistics even when lowering the SC exhibited improvements to the precision of the internal data set. Some of the improvements to the validation may come from better data coverage, but uncertainties inherent in the indicators and stressor layers themselves also should be considered.
Screening-level risk assessments often contain uncaptured uncertainties due to lack of effects data (Maruya et al. 2014). However, the data used here were relatively comprehensive in spatial coverage and provided multiple indicator types for analysis on the effects side and expert-derived threat layers for examining exposure. One of the benefits of using the Reef Check and WRI data sets is the cohesiveness of the measurements. The shared protocol for reef measurements used by Reef Check provided data for multiple types of indicators across the entire world and for many coral reefs. Localized sampling efforts or even countrywide sampling efforts are often not integrated to this extent. Sampling sites were compared between the Reef Check data from this time period and the reef locations in Burke et al. (2011), and several areas were found to not have Reef Check sample sites in the region. Data coverage for the Reef Check endpoints did not encompass many key reef areas globally. Therefore, it was assumed that existing measurements for reefs represent those without data. For example, Australia lacked coverage over some of the coastline and reefs near Papua New Guinea and the Timor Sea, but outlying reefs Christmas Island and Cocos (Keeling) Islands had sampling locations. In some areas, coverage was spotty in large coastal regions. This was observed in areas of the Indian Ocean such as parts of the coastline of Kenya, Mozambique, India, Madagascar, Tanzania, and island chains. Missing data on coral reefs throughout the world could have impacted the results by not including coral reefs that are more or less sensitive to the local or global reef threats. The Reef Check sampling protocol advises having at least 1 site representing the healthiest coral reefs in regions and selecting additional sites for comparison with human impacts (Hodgson et al. 2006). This may have helped provide a gradient of impacts for comparison of changes to reef condition with changes to WRI threat levels. The areas missing coverage can be targeted for future sampling efforts to refine the regional analyses.
Summary statistics such as the maximum for all negative measurement indicators and the average for positive indicators were assumed to be representative and of similar resolution as the static threat layers used from Burke et al. (2011). For reefs with time series data, this does not adequately capture events or the time course of changes. By using the maximum extent of bleaching, it was hoped that the temporal coverage of the Reef Check database adequately captured bleaching events for the time period assessed. Temporal measurements were unbalanced over the time period, with some reefs having regular monitoring and others having single sampling events. The summary statistics used add to the uncertainties in the analysis; however, the global and regional coverage in the current database might allow the discernment of broad patterns across the existing regions sampled. Likewise, the stressor layers and risk estimates are an insightful starting point for more detailed examinations. Multiple available sources of global evidence were used to infer oceanic threats, but Burke et al. (2011) lists the limitations in the threat maps, including aspects that are underestimated or not fully incorporated and that can be considered with the uncertainties in the model.
The approach here may be useful for examining indicators of coral reef and other resource conditions from existing global spatial data. The results from the global, all data networks did not always capture the regional relationships, supporting the decision to analyze region-specific data. This observation could also be important to consider for examining local coral reef relationships that the regional models might not predict. The naïve-aligned models facilitate connecting the target variable with each predictor for a more direct relationship analysis than a multilayered BN. The work was screening level and managing reef health would require greater explanatory depth such as causal modeling. However, screening-level assessments can be used to determine where sensitivities are high enough to prompt action, future data gathering, and the need and scope of future assessments (Suter 2007). Additional data can provide probabilities of risk with changes in stressors over space and time, but screening-level risk assessments can interpret past data for supporting prioritization and broad understanding of potential relationships with local and global threats. Although how this information may be used is dependent on the scale and context of the management questions and must consider the drawbacks in the data and uncertainties outside of the model, some of the results here may be useful as a starting point for managers to initially prioritize an investigation of stressors that can impact reef resiliency or health.
Innovative monitoring that is responsive to management needs and adaptive management by considering more ecosystem processes will improve available solutions for protecting reefs (Hughes et al. 2011). When coupled with BNs, a broader management approach can update known relationships and knowledge about coral reef stressors with a comprehensive, causal risk assessment. Targeted data gathering can be used to bolster monitoring systems like Reef Check to provide information to test risk hypotheses and evaluate management performance before and after interventions are taken (NASEM 2019). In conjunction with data collection, systematic reviews could also support a risk-based approach where prior information from the reviews are used to identify data gaps and build initial distributions and BN structures to be modified or tested with new information. Exemplary information reviews that have been conducted for establishing effect sizes from interventions in watersheds and at sea to support management goals (e.g., Sciberras et al. 2013) can provide frameworks for such work.
Although the work in this is exploratory, the model development methods can be adapted and developed to better assess the influence of local and global stressors on coral reef condition. From a Bayesian perspective, this may provide a prior probability of risks that can be updated with new data. Future work can include additional endpoints directly and indirectly related to coral reef health and sensitivity to the stressors. These include commercially and ecologically important fish species and invertebrates along with coral reefs sensitive to specific stressors and keystone coral reefs that may be facing global threats. Future global screening risk assessments that compare the sensitivity of different coral reef endpoints to stressors and management effectiveness will further identify evidence needs that support management decisions from the assessments.
Supplementary Material
Acknowledgment—
The authors declare no conflict of interest. The authors received no external funding for this work. The views expressed in this article are those of the authors and do not necessarily represent the views or policies of the US Environmental Protection Agency. This document has been reviewed in accordance with US Environmental Protection Agency policy and approved for publication. Links to websites outside the USEPA website are provided for the convenience of the user. Inclusion of information about a website, an organization, a product or a service does not represent endorsement or approval by USEPA, nor does it represent USEPA opinion, policy or guidance unless specifically indicated. USEPA does not exercise any editorial control over the information that may be found at any non-USEPA website. Any mention of trade names, manufacturers, or products does not imply an endorsement by the United States Government or the US Environmental Protection Agency. The USEPA and its employees do not endorse any commercial products, services, or enterprises. The authors thank Stefan Conrady, Justin Bousquin, Jannicke Moe, Miriam Glendell, and anonymous journal reviewers for helpful comments on earlier drafts of this manuscript.
Footnotes
Publisher's Disclaimer: Disclaimer—The peer review for this article was managed by the Editorial Board without the involvement of JF Carriger.
SUPPLEMENTAL DATA
Supplemental Data File 1 contains 2 additional figures. Supplemental Data File 2 contains validation measures for candidate networks, sensitivity measures, prior mean plots with sensitivity measures, TMA plots, and network conditional probability tables.
Data Availability Statement—
Data used for developing the Bayesian networks will be publicly available from the US Environmental Protection Agency’s ScienceHub. The Supplemental Data contain all conditional probability tables for the Bayesian networks used for the output in the article so the networks themselves can be reproduced in any Bayesian network software.
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Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
Data used for developing the Bayesian networks will be publicly available from the US Environmental Protection Agency’s ScienceHub. The Supplemental Data contain all conditional probability tables for the Bayesian networks used for the output in the article so the networks themselves can be reproduced in any Bayesian network software.